Sort of. You can have as many devices as you need on your unlimited internet access account but only one at a time can be connected.
Last cruise, my wife and I swapped log-ins as needed. When switching from one device to another, you don't need to log off the current device first; when you try to connect the second device, it will tell you you're still connected to the first device and ask you if it's OK to log off and connect you to the second device.
And, at least in our case, we both continued to be able to send and receive texts even when we were logged off. Don't know if that's a Princess bug or feature.